As can be surmised, all the numbers from zero through nine have been substituted by some letter from the set, J,L,M,N,R,S,T,U,X, and Y. Not only was the solution difficult, but so was Sutton's finding a simple long division that contained all the digits. In this age of spreadsheets and calculators, it's rare when a person does a long division by hand. While long division by hand seems inelegant, a longer step from elegance was my decision to solve this problem by a brute forcecomputer program.

A brute force attack, also called a proof by exhaustion and a proof by cases, involves checking each possible case. One famous example of a brute force attack is the computer-assisted proof of the Four-Color Conjecture that you need only four colors to color a map such that no adjacent regions have the same color. This conjecture was not easy to prove analytically, but Kenneth Appel and Wolfgang Haken used a computer to analyze every conceivable map to prove the conjecture true in 1976.[9-10] They analyzed all 1,936 cases of the problem using available computers of that time, an IBM 360-75, an IBM 370-158, and an IBM 370-168.[10]

The Sutton long division has ten variables, each of which has ten possible values. This long division requires the four equations shown below to be simultaneously true. This leads to 1010 (ten billion) cases involving four calculations each. The C language program that I wrote is a trivial assemblage of ten nested loops (source code, here, shannon.c).

My son, who's an actual computer scientist, produced an improved version of the program, with source code here, shannon2.c. His program obtains the solution in 0.605299 seconds, nearly five times faster, on my desktop computer.